The perceptual probability¹, chance, and odds, of two independent murders of female adults, by way of 'Cut Throat', occurring within the same hour, within the observed 'killing field' of 'Jack the Ripper'
¹ i.e. the probability, chance, and odds that I believe should have been perceived, at the onset of 1888
---
Please Note:
I am presenting calculated estimations of the perceptual odds, chances, and probabilities, that I believe should prevail, in any effort to gauge the extraordinary nature of the so-called 'Double Event'; as opposed to calculations of the actual odds, chances, and probabilities, that do prevail, in any analysis of ... let's say ... the toss of a coin.
In other words: I am effectively presenting 'theory', as opposed to 'reality'.
When a human being resolves to commit murder, ... all bets are off. Probability will not stand in his way, or affect his resolution.
But, probability theory is certainly a viable means of gauging any sort of extraordinary nature that his resolution might posses, with regard to timing and/or placement.
---
In the five calendar-years prior to 1888, there were a total of twenty two (22) registered deaths of female adults, throughout the whole of England, classified as 'Murder', by way of 'Cut Throat': i.e. an average of 4.40 such registered deaths, per annum.
So, a reasonable expectation, at the onset of 1888, would have been that four (4) deaths of female adults, classified as 'Murder', by way of 'Cut Throat', would be registered, throughout England, during the coming year.
However, for the sake of more accurate estimation, of the perceptual odds that two female adults would be murdered independently, by way of 'Cut Throat', within the aforementioned color-shaded region, ... and, within the same hour, during the coming year; the calculated average of 4.40 will be utilized.
---
Cumulative Probability Distribution (Murder-Site Mean-Center (Green Dot) -to- Greatest Observed Deviation (Mary Ann Nichols Murder-Site)) (Circular) (Click Image, to Enlarge in flickr)
Underlying Aerial Imagery: Copyright Google Earth, 2007
Overlying Plots, Labels and Color-Shadings: Copyright Colin C. Roberts, 2010
The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region
- Assume a Population of 27,482,104, for the Whole of England, in Accordance with the Census of England & Wales, 1891
- Assume a Population of 120,000*, for the depicted Color-Shaded Circular Region, in Accordance with the Census of England & Wales, 1891; and Charles Booth's "Labour & Life of the People: London", Appendix to Volume II, Williams & Norgate, 1891
- Calculate the Number of Regions that Must be Drawn, in order to Divide England's Total Population, of 27,482,104; into Sub-Sets that Consist of 120,000 Persons: 27,482,104 ÷ 120,000 = 229.02
- Calculate the Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region: 4.40 ÷ 229.02 = 0.01921250 (i.e. 1.921250%)
* I have estimated the population, of the depicted color-shaded circular region, to have been between 90,000 and 120,000, in 1888
- Perceptual Probability: 1.921250%
---
The Perceptual Chance that One Murder, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.01921250) = 1 / 52.05 (i.e. 1 -in- 52.05)
- Perceptual Chance: 1 -in- 52.05
---
The Perceptual Odds that One Murder, ...
- Calculate the Perceptual Odds: (52.05 - 1) -to- 1 (i.e. 51.05 -to- 1)
- Perceptual Odds: 51.05 -to- 1
---
Again; ...
That One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region:
- Perceptual Probability: 1.921250%
- Perceptual Chance: 1 -in- 52.05
- Perceptual Odds: 51.05 -to- 1
---------
The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, during a particular One-Hour Period
- Assume Three Hundred and Sixty Five (365)* Twenty-Four-Hour Periods, per Year
- Assume Eight (8) 'Prime Throat-Cutting Hours' (i.e. 10:00PM - 6:00AM), per Twenty-Four-Hour Period
- Calculate the Number of 'Prime Throat-Cutting Hours' (i.e. 10:00PM - 6:00AM), per Year: 365 x 8 = 2,920
- Calculate the Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, during a particular One-Hour Period; i.e. during a particular 'Prime Throat-Cutting Hour': 4.40 ÷ 2,920 = 0.00150685 (i.e. 0.150685%)
* Calendar-Year 1888 was, in fact, a 'Leap-Year'; and consisted, therefore, of three hundred and sixty six (366) twenty-four-hour periods
- Perceptual Probability: 0.150685%
---
The Perceptual Chance that One Murder, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.00150685) = 1 / 663.64 (i.e. 1 -in- 663.64)
- Perceptual Chance: 1 -in- 663.64
---
The Perceptual Odds that One Murder, ...
- Calculate the Perceptual Odds: (663.64 - 1) -to- 1 (i.e. 662.64 -to- 1)
- Perceptual Odds: 662.64 -to- 1
---
Again; ...
That One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, during a particular One-Hour Period:
- Perceptual Probability: 0.150685%
- Perceptual Chance: 1 -in- 663.64
- Perceptual Odds: 662.64 -to- 1
---------
The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period
This involves a 'Joint Probability', with respect to the first, of four possible outcomes:
1.) Region 'Yes', Hour 'Yes'
2.) Region 'Yes', Hour 'No'
3.) Region 'No', Hour 'No'
4.) Region 'No', Hour 'Yes'
- Calculate The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period: 1.921250% x 0.150685% = 0.002895%
- Perceptual Probability: 0.002895%
---
The Perceptual Chance that One Murder, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.00002895) = 1 / 34,541.90 (i.e. 1 -in- 34,541.90)
- Perceptual Chance: 1 -in- 34,541.90
---
The Perceptual Odds that One Murder, ...
- Calculate the Perceptual Odds: (34,541.90 - 1) -to- 1 (i.e. 34,540.90 -to- 1)
- Perceptual Odds: 34,540.90 -to- 1
---
Again; ...
That One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period:
- Perceptual Probability: 0.002895%
- Perceptual Chance: 1 -in- 34,541.90
- Perceptual Odds: 34,540.90 -to- 1
---------
The Perceptual Probability that Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period
This involves a 'Joint Probability', with respect to the first, of four possible outcomes:
1.) First Murder 'Yes', Second Murder 'Yes'
2.) First Murder 'Yes', Second Murder 'No'
3.) First Murder 'No', Second Murder 'No'
4.) First Murder 'No', Second Murder 'Yes'
- Calculate The Perceptual Probability that Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period: 0.002895% x 0.002895% = 0.000000083812%
- Perceptual Probability: 0.000000083812%
---
The Perceptual Chance that Two Independent Murders, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.00000000083812) = 1 / 1,193,142,903.19 (i.e. 1 -in- 1,193,142,903.19)
- Perceptual Chance: 1 -in- 1,193,142,903.19
---
The Perceptual Odds that Two Independent Murders, ...
- Calculate the Perceptual Odds: (1,193,142,903.19 - 1) -to- 1 (i.e. 1,193,142,902.19 -to- 1)
- Perceptual Odds: 1,193,142,902.19 -to- 1
---
Again; ...
That Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period:
- Perceptual Probability: 0.000000083812%
- Perceptual Chance: 1 -in- 1,193,142,903.19
- Perceptual Odds: 1,193,142,902.19 -to- 1
~~~
The perceptual odds, i.e. the odds of such an occurrence that should have been perceived, at the onset of 1888, are indeed, astronomical!
- They are slightly greater than the odds of thirty (30) sequential tosses of a coin, landing entirely on 'Heads'.
- They are significantly greater than the odds of ten (10) sequential tosses of a single die, landing entirely on '1'.
~~~
Again:
I have presented calculated estimations of the perceptual odds, chances, and probabilities, that I believe should prevail, in any effort to gauge the extraordinary nature of the so-called 'Double Event'; as opposed to calculations of the actual odds, chances, and probabilities, that do prevail, in any analysis of ... let's say ... the toss of a coin.
In other words: I have effectively presented 'theory', as opposed to 'reality'.
¹ i.e. the probability, chance, and odds that I believe should have been perceived, at the onset of 1888
---
Please Note:
I am presenting calculated estimations of the perceptual odds, chances, and probabilities, that I believe should prevail, in any effort to gauge the extraordinary nature of the so-called 'Double Event'; as opposed to calculations of the actual odds, chances, and probabilities, that do prevail, in any analysis of ... let's say ... the toss of a coin.
In other words: I am effectively presenting 'theory', as opposed to 'reality'.
When a human being resolves to commit murder, ... all bets are off. Probability will not stand in his way, or affect his resolution.
But, probability theory is certainly a viable means of gauging any sort of extraordinary nature that his resolution might posses, with regard to timing and/or placement.
---
In the five calendar-years prior to 1888, there were a total of twenty two (22) registered deaths of female adults, throughout the whole of England, classified as 'Murder', by way of 'Cut Throat': i.e. an average of 4.40 such registered deaths, per annum.
So, a reasonable expectation, at the onset of 1888, would have been that four (4) deaths of female adults, classified as 'Murder', by way of 'Cut Throat', would be registered, throughout England, during the coming year.
However, for the sake of more accurate estimation, of the perceptual odds that two female adults would be murdered independently, by way of 'Cut Throat', within the aforementioned color-shaded region, ... and, within the same hour, during the coming year; the calculated average of 4.40 will be utilized.
---
Cumulative Probability Distribution (Murder-Site Mean-Center (Green Dot) -to- Greatest Observed Deviation (Mary Ann Nichols Murder-Site)) (Circular) (Click Image, to Enlarge in flickr)
Underlying Aerial Imagery: Copyright Google Earth, 2007
Overlying Plots, Labels and Color-Shadings: Copyright Colin C. Roberts, 2010
The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region
- Assume a Population of 27,482,104, for the Whole of England, in Accordance with the Census of England & Wales, 1891
- Assume a Population of 120,000*, for the depicted Color-Shaded Circular Region, in Accordance with the Census of England & Wales, 1891; and Charles Booth's "Labour & Life of the People: London", Appendix to Volume II, Williams & Norgate, 1891
- Calculate the Number of Regions that Must be Drawn, in order to Divide England's Total Population, of 27,482,104; into Sub-Sets that Consist of 120,000 Persons: 27,482,104 ÷ 120,000 = 229.02
- Calculate the Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region: 4.40 ÷ 229.02 = 0.01921250 (i.e. 1.921250%)
* I have estimated the population, of the depicted color-shaded circular region, to have been between 90,000 and 120,000, in 1888
- Perceptual Probability: 1.921250%
---
The Perceptual Chance that One Murder, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.01921250) = 1 / 52.05 (i.e. 1 -in- 52.05)
- Perceptual Chance: 1 -in- 52.05
---
The Perceptual Odds that One Murder, ...
- Calculate the Perceptual Odds: (52.05 - 1) -to- 1 (i.e. 51.05 -to- 1)
- Perceptual Odds: 51.05 -to- 1
---
Again; ...
That One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region:
- Perceptual Probability: 1.921250%
- Perceptual Chance: 1 -in- 52.05
- Perceptual Odds: 51.05 -to- 1
---------
The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, during a particular One-Hour Period
- Assume Three Hundred and Sixty Five (365)* Twenty-Four-Hour Periods, per Year
- Assume Eight (8) 'Prime Throat-Cutting Hours' (i.e. 10:00PM - 6:00AM), per Twenty-Four-Hour Period
- Calculate the Number of 'Prime Throat-Cutting Hours' (i.e. 10:00PM - 6:00AM), per Year: 365 x 8 = 2,920
- Calculate the Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, during a particular One-Hour Period; i.e. during a particular 'Prime Throat-Cutting Hour': 4.40 ÷ 2,920 = 0.00150685 (i.e. 0.150685%)
* Calendar-Year 1888 was, in fact, a 'Leap-Year'; and consisted, therefore, of three hundred and sixty six (366) twenty-four-hour periods
- Perceptual Probability: 0.150685%
---
The Perceptual Chance that One Murder, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.00150685) = 1 / 663.64 (i.e. 1 -in- 663.64)
- Perceptual Chance: 1 -in- 663.64
---
The Perceptual Odds that One Murder, ...
- Calculate the Perceptual Odds: (663.64 - 1) -to- 1 (i.e. 662.64 -to- 1)
- Perceptual Odds: 662.64 -to- 1
---
Again; ...
That One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, during a particular One-Hour Period:
- Perceptual Probability: 0.150685%
- Perceptual Chance: 1 -in- 663.64
- Perceptual Odds: 662.64 -to- 1
---------
The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period
This involves a 'Joint Probability', with respect to the first, of four possible outcomes:
1.) Region 'Yes', Hour 'Yes'
2.) Region 'Yes', Hour 'No'
3.) Region 'No', Hour 'No'
4.) Region 'No', Hour 'Yes'
- Calculate The Perceptual Probability that One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period: 1.921250% x 0.150685% = 0.002895%
- Perceptual Probability: 0.002895%
---
The Perceptual Chance that One Murder, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.00002895) = 1 / 34,541.90 (i.e. 1 -in- 34,541.90)
- Perceptual Chance: 1 -in- 34,541.90
---
The Perceptual Odds that One Murder, ...
- Calculate the Perceptual Odds: (34,541.90 - 1) -to- 1 (i.e. 34,540.90 -to- 1)
- Perceptual Odds: 34,540.90 -to- 1
---
Again; ...
That One Murder, of a Female Adult, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period:
- Perceptual Probability: 0.002895%
- Perceptual Chance: 1 -in- 34,541.90
- Perceptual Odds: 34,540.90 -to- 1
---------
The Perceptual Probability that Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period
This involves a 'Joint Probability', with respect to the first, of four possible outcomes:
1.) First Murder 'Yes', Second Murder 'Yes'
2.) First Murder 'Yes', Second Murder 'No'
3.) First Murder 'No', Second Murder 'No'
4.) First Murder 'No', Second Murder 'Yes'
- Calculate The Perceptual Probability that Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period: 0.002895% x 0.002895% = 0.000000083812%
- Perceptual Probability: 0.000000083812%
---
The Perceptual Chance that Two Independent Murders, ...
- Calculate the Perceptual Chance: 1 ÷ (1 ÷ 0.00000000083812) = 1 / 1,193,142,903.19 (i.e. 1 -in- 1,193,142,903.19)
- Perceptual Chance: 1 -in- 1,193,142,903.19
---
The Perceptual Odds that Two Independent Murders, ...
- Calculate the Perceptual Odds: (1,193,142,903.19 - 1) -to- 1 (i.e. 1,193,142,902.19 -to- 1)
- Perceptual Odds: 1,193,142,902.19 -to- 1
---
Again; ...
That Two Independent Murders, of Female Adults, by way of 'Cut Throat', would Occur, within the depicted Color-Shaded Circular Region; and during a particular One-Hour Period:
- Perceptual Probability: 0.000000083812%
- Perceptual Chance: 1 -in- 1,193,142,903.19
- Perceptual Odds: 1,193,142,902.19 -to- 1
~~~
The perceptual odds, i.e. the odds of such an occurrence that should have been perceived, at the onset of 1888, are indeed, astronomical!
- They are slightly greater than the odds of thirty (30) sequential tosses of a coin, landing entirely on 'Heads'.
- They are significantly greater than the odds of ten (10) sequential tosses of a single die, landing entirely on '1'.
~~~
Again:
I have presented calculated estimations of the perceptual odds, chances, and probabilities, that I believe should prevail, in any effort to gauge the extraordinary nature of the so-called 'Double Event'; as opposed to calculations of the actual odds, chances, and probabilities, that do prevail, in any analysis of ... let's say ... the toss of a coin.
In other words: I have effectively presented 'theory', as opposed to 'reality'.
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